This invention relates generally to magnetic resonance imaging and more particularly the invention relates to gradient waveforms for use in magnetic resonance imaging.
Nuclear magnetic resonance (NMR) imaging, also called magnetic resonance imaging (MRI), is a non-destructive method for the analysis of materials and represents a new approach to medical imaging. It is completely non-invasive and does not involve ionizing radiation. In very general terms, nuclear magnetic moments are excited at specific spin precession frequencies which are proportional to the local magnetic field. The radio-frequency signals resulting from the precession of these spins are received using pickup coils. By manipulating the magnetic fields, an array of signals is provided representing different regions of the volume. These are combined to produce a volumetric image of the nuclear spin density of the body.
Briefly, a strong static magnetic field is employed to line up atoms whose nuclei have an odd number of protons and/or neutrons, that is, have spin angular momentum and a magnetic dipole moment. A second RF magnetic field, applied as a single pulse transverse to the first, is then used to pump energy into these nuclei, flipping them over, for example to 90.degree. or 180.degree.. After excitation, the nuclei gradually return to alignment with the static field and give up the energy in the form of weak but detectable free induction decay (FID). These FID signals are used by a computer to produce images.
The excitation frequency, and the FID frequency, is defined by the Larmor relationship which states that the angular frequency .omega..sub.o, of the precession of the nuclei is the product of the magnetic field B.sub.o, and the so-called magnetogyric ratio, .gamma., a fundamental physical constant for each nuclear species: EQU .omega..sub.o=B.sub.o .multidot..gamma.
Accordingly, by superimposing a linear gradient field, B.sub.z =Z.multidot.G.sub.z on the static uniform field, B.sub.o, which defines the Z axis, for example, nuclei in a selected X-Y plane can be excited by proper choice of the frequency spectrum of the transverse excitation field applied along the X or Y axis. Similarly, a gradient field can be applied in the X-Y plane during detection of the FID signals to spatially localize the FID signals in the plane. The angle of nuclear spin flip in response to an RF pulse excitation is proportional to the integral of the pulse over time.
In-magnetic resonance imaging (MRI), the k-space formalism is used to design and analyze readout gradients and excitation gradients. During signal readout, a series of samples in k-space (or Fourier transform space) are acquired. The location in k-space where a particular sample is acquired is proportional to the integral of the readout gradient up to that time. In this application, we discuss the design of gradient waveforms using a particular algorithm. For concreteness, we discuss the design of gradients for spiral scans of k-space, but the technique can be used for the design of other scans as well, subject to certain constraints.
Spiral scans are an efficient way to cover k-space and have certain other advantages, such as good behavior in the presence of moving material such as flowing blood. They were first suggested by Likes and later independently by Ljunggren. Macovski proposed certain improvements, such as constant-linear-velocity spiral scans. Buonocore proposed a method for designing accelerated spiral gradients, see U.S. Pat. No. 4,651,096. Pauly suggested using spiral scans for selective excitation and designed constant-slew spiral gradients using an iterative approach. Hardy and Cline discussed another iterative method for designing constant-slew spiral gradients. Meyer et al. designed spiral readout gradients using both slew and amplitude constraints using an iterative technique. Spielman and Pauly and King described iterative methods for constant-voltage spiral readout gradients. Meyer and Macovski and Spielman et al. discussed the iterative design of spiral readout gradients with variable sampling densities. Meyer described the iterative design of spiral-in/spiral-out readout gradients. Heid described an approximate analytical framework for constant-slew readout gradients.
There are an infinite number of gradient waveforms that trace out a particular spiral K-space trajectory. The design of these gradient waveforms is an important element of spiral scanning, and a number of iterative approaches have been successfully applied to this problem. The present invention presents an analytical, non-iterative, graphical solution to this problem. This approach is much faster and more intuitive than earlier approaches. It easily incorporates different gradient circuit models and can lead to better designs than approaches that do not use the geometry of the problem.